Lesson 8.6

Page 634-636

#1-21 (ODD), 23-31 (EOO), 33-45 (ODD), 47-55 (EOO), 57-69 (ODD)

Pick up the handout on the table

Counting Principles

Objective

Students will know how to solve counting problems using the Fundamental Counting Principle, permutations, and combinations.

A deli offers 4 types of meat (ham, turkey, roast beef, and pastrami), 3 types of bread (white,

wheat, and rye), and 2 types of cheese (cheddar and Swiss). How many different

types of sandwiches can you make?

Tree Diagram

What relationship do you notice between the number of options of meat, bread, and cheese with the number of

different types of sandwiches?

If one event can occur in m ways and another event can occur in n ways, then the number of

ways that both events can occur is m • n.

This principle can be extended to 3 or more events as well.

Fundamental Counting Principle

In how many different ways can you order the letters A, B, and C?

6

Permutation - an ordering of n objects.

The number of permutations of n distinct objects is:

n!

factorial

n(n 1)(n 2)...321

** 0!1

Verify using your calculator.

The number of distinguishable permutations of n objects where one object is repeated q1 times, and another is repeated q2 times, and so on is:

Permutations with Repetitions

n!q1!q2!...qk!

Use the letters A, B, C, D, E, and F.

Combination - is a selection of r objects from a group of n objects where the order is not important.

Combinations of n Objects Taken r at a Time

The number of combinations of r objects taken from a group of n distinct objects is denoted by

nCr and is given by:

!!!rrn

nC

rn

Verify using your calculator.